Determine if Rolle's Theorem can be ap- plied to f(x) = x² + 3x - 18 x + 3 on the interval [-6, 3], and if it can, find all numbers c satisfying the conclusion of that theorem.

Q: Determine whether the planes are parallel, orthogonal, or neither. 3x 15y 3z = 8 4x20y4z = -2 - O…

A: Two lines are parallel if the ratio between their corresponding coefficients is same. The angle…

Q: Find the derivate a) F(x) = 5-8x 1+ 2X f'(x)= 6) write all x-values (if any) at which the tangent…

A: (a) f(x)=5-8x1+2xd dx(ab)=bdadx-adbdxb2d dx(xn)=nxn-1

Q: Let f(x) = -12x sin(x) cos(x). f'(x) at x = ³7. 2 Evaluate ƒ'( ³ ) =

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Q: Let a = (-3, -5, -2) and 6 = (2, 5, 3). Find a x b. <-5 X, 5 ✔25

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Consider the function f(x,y)=e^4x−x^2−4y−y^2. Find and classify all critical points of the…

A: Given function:- fx,y=e4x−x2−4y−y2

Q: After walking through the fifth gate, your computer informs you that more than half of the gates…

A: Given function f( t ) = 1a( 2t3 - 15t2 + 45 )

Q: Consider the following planes. -2x + y + z = 2 10x - 5y + 2z = 4 (a) Find the angle between the two…

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Q: The data in the table concerns the lactonization of hydroxyvaleric acid at 25°C. They give the…

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Q: The position function of a particle is given below. s(t) = t³ + 6t² − 33t, t ≥ - 0 When does the…

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Q: Find the critical points in the domain of the function f(x) = 8x³ - 7x.

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Q: Find the general solution for the differential equation. dy dx + 2xy = 11x

A: Given,            The differential equation is dydx+2xy=11x.To find : Find the general solution for…

Q: Find the equation of the tangent line T to the graph of f(x) = 8 sinx at the given point (6,8 sin…

A: given  f(x)=8sinx d dx(sinx)=cosxstandard form of quation is y-y1=m(x-x1)where m is slope m=f'(x)

Q: Differentiate the function. g(t) = 4t-1/8 g'(t) =

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Q: 3. Use the Root Test or the Ratio Test to determine whether the series is absolutely convergent,…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=2-2².…

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Q: F(x) f(x) 1 + f²(x)*

A: Given, F(x) = f(x)1 + f2(x) f'(x) is defined for all x∈[a,b]|f(x)| &lt; 1 for all x∈[a,b]That is,-1…

Q: Urves with more than two asymptotes and/or oblique asymptotes: k a) Graph y ==+x and y = X k where…

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Q: (4) The position function of a ball dropped from a building is given by s(t) = 16t² - 144. (a)…

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Q: Differentiate the function with respe z' = Z A .6 yo + Bey

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Q: The relationship between the price and the demand of a certain product is described by the equation…

A: Given price function  p + 0.03x = 143  p = 143 - 0.03x

Q: 4. Find the length of the logarithmic spiral r = e ¹2 from 0=0 to 0=2

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Q: 6. What principal invested at 13% compounded continuously for 6 years will yield $9000? Round the…

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Q: Let f(x) = 8x³ + 1. Find the open intervals on which f is increasing (decreasing). Then determine…

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Q: Solve yy'= -(x+2),Y(0)=\

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Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

A: As we know that, To expression to calculate the equation of the plane when it passes through the…

Q: Find an equation of the tangent line to the graph of the given function at the specified point. x²-1…

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Q: 8. Solve the following. (a) Find the equation of the tangent line to the graph of f(x) = x²-9 at x =…

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Q: G(x) = − 1x². +3 H (x) = − 1x² – 7 M (x) = − 1x² + 1/

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Q: Find the derivate of this function]: 2 a) f(x) = 4x² + x + 9 at -5 f(-5) = b) f(x) = √√√x at 16 F'…

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Q: 3. Determine whether the series is convergent or divergent. State which test for convergence or…

A: SOLUTION: Given that ∑k=1∞ke-k2 Now we have to determine whether the series is convergent or not .…

Q: Solve for b. Use all lower case letters. -(a + b) b = S =

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Q: Find the region generated by rotating the region bounded by xy=1, x=1, x=2 and y=0 around the y-axis

A: Given :- The region bounded by xy=1, x=1, x=2 and y=0 To find :- The region

Q: Solve the equation for the indicated variable. (Enter your answers as a comma-separated list a² + b²…

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Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

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Q: he given curve is rotated about the y-axis. Find the area of the resulting surface. y =  1 3x3/2,…

A: Given

Q: Determine the truth set of the predicate: P(x): x € R/ x² − 3x + 1 = 0: 2 Solution: This is {x € R |…

A: Given Predicate: P(x) : x∈R ∧ x2-3x+1=0 To find: The truth set of P(x)

Q: Find the cross product a x b. a =j + 6k, b = 5i - j + 4k Verify that it is orthogonal to both a and…

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Q: Find the Maclaurin series and find the interval on which the expansion is valid. f(x) = ln (1-x²)

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Q: Consider the following. Sk (4x - y) da, where R is the region in the first quadrant enclosed by the…

A: Given that  R is the region in the first quadrant enclosed by the circle x2+y2=4and the lines x=0…

Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

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Q: 3 Functions fand g are defined by f(x)= XER and |x| |x|+3x 2 g(x)= respectively. (a) Express…

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Q: let y = 5 log2 x³ find y' O 15/(In2 +x) O 15/x O (5/In2)(3/x) noe of the above

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Q: Let à = (-3, -5, -2) and 6 = (2, 5, 3). Find à x b. V Calculator Check Answer 7

A: Please see the below picture for detailed solution.

Q: Find the derivatives of the following functions. sec5 (x) 1- x-7 (a) g(x) g'(x) = (b)x= dx dt = = 1…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y=x and y=2-x…

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Q: A spherical balloon is being inflated in such a way that the radius of the balloon is increasing at…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Verify that the given differential equation is exact; then solve it. (21x²y³ + 4y) dx + (21x³y² + 4y…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as a…

Q: ← Give integers p and q such that Nul A is a subspace of RP and Col A is a subspace of Rª. A = 1 245…

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Q: After traversing your continuous path, you finally arrive at Gate 5. Your computer reads the gate's…

A: Given that , fx=x6-2x , gx=x2+4x-59 , hx=2x-11 and mx=fx·gx , nx=gxhx